@gball I will post up links later on when I get back home.
Here's a couple of just general forum discussions that I still had open where a Les Paul goes both sharp and flat:
I have a 2009 Les Paul Studio with Gold Hardware that will not stay in tune, and is very hard to get into tune. I just put new strings on it, gibson vintage reissue and it is a little better. But just sitting around the 1st three strings go shart, 4 and 5 go flat and 6 does both. No pattern that ...
forum.gibson.com
I've had my Les Paul Standard for around 4 months now and I still have tuning issues with it. Tune it up at home, go up to the church take it out of the case and the thing has gone sharp. Retune, 10 minutes later it's flat. Makes me wonder if the Autotune system that they had on the 2015 models...
bluesguitarunleashed.com
In an interview video that I posted earlier, Smith said the reason he started looking at Jackson's was because he "couldn't keep his Les Paul in tune."
Now, maybe having to tune between every song is normal, but it's funny in a way that my 1987 Squire - under the same conditions - stayed in tune even using the stock unlocking tremolo.